Parametric optimization with applications to optimal control and sequential quadratic programming

W. Alt: Parametric optimization with applications to optimal control and sequential quadratic programming
in: Department of Mathematics, University of Bayreuth (eds.)
Bayreuther Mathematische Schriften 35, Bayreuth, Germany, 1991, 1 - 37

Smart-Link: http://bms.math.uni-bayreuth.de/all_books.html#vol_35
ISBN/ISSN/ISMV Nummer: 0172-1062
MR Nummer: 1104518
Zentralblattnummer: 0734.90094
Keywords: nonlinear optimization; parametric programming; stability of solutions; optimal control; Lagrange-Newton method; sequential quadratic programming
Mathematics Subject Classification Code: 49B50 (49D05 49D15)


Abstract:

We investigate existence, uniqueness and continuity of solutions to nonlinear parametric optimization problems in Banach spaces. Using an implicit function theorem for strongly regular generalized equations it is shown that if constraint regularity, a stability condition for the multipliers and a strong second-order sufficient optimality condition hold at a local minimizer, then for sufficiently smooth perturbations of the constraints and the objective function the optimal solutions and the associated multipliers are locally single valued and continuous functions of the parameter. The results are applied to investigate stability of optimal control problems and local convergence properties of a sequential quadratic programming method for infinite-dimensional optimization problems.

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